Consider an electron in the 5 f state of a hydrogen atom. When the ground state

Question

Consider an electron in the 5f state of a hydrogen atom. When the ground state energy is -13.6 eV, the energy of the atom is -0.544 eV. In the quantum mechanical description of the atom, what are:

(a) the magnitude of the orbital angular momentum of the electron, in terms of h?

(b) the largest possible value for the z-component of the angular mometum of the electron, in terms of h?

***The solutions/answers are (a) 3.46h and (b) 3h ...I've got no clue what "ground state energy" and "energy of the atom" are trying to tell us. Also, what is the difference bewteen an "orbital angular momentum" and a "z-component of an angular momentum"?...I'm pretty lost on what this problem is asking for***

***Please provide ALL concepts/formulas used***

Explanation / Answer

The energy of the hydrozen atom   in 5f state is    - 0.544 eV   (a) The   f orbital has   orbital angular momentum quantum number value   3   The magnitude of the orbital angular momentum                     L   = sqrt (  l   (l+1) ) h (bar )                         L   =   sqrt (  3 ( 3+1) )   h (bar )      =   3.46  h (bar )   (b) The   z componet of L     is Lz   = + m h (bar )     (or) - m h (bar ) Here m can take value   from      -l   .....,0 , +l our given value   for   l   = 3 hence    m has values      -3 ,-2 ,1 ,0   1, 2, 3 Hence    maximum possible   z componet of L (angular momentum is )   =   +3 h (bar )

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